US9355649B2 - Sound alignment using timing information - Google Patents
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- US9355649B2 US9355649B2 US13/675,711 US201213675711A US9355649B2 US 9355649 B2 US9355649 B2 US 9355649B2 US 201213675711 A US201213675711 A US 201213675711A US 9355649 B2 US9355649 B2 US 9355649B2
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Definitions
- Sound alignment may be leveraged to support a wide range of functionality. For example, sound data may be captured for use as part of a movie, recording of a song, and so on. Parts of the sound data, however, may reflect capture in a noisy environment. Therefore, noise may interfere with consumption of desired parts of the sound data, such as to understand a speaker in a lecture, a band in a live concert, and so forth. Accordingly, parts of the sound data may be replaced by other sound data using sound alignment. Sound alignment may also be employed to support other functionality, such as to utilize a foreign overdub to replace the sound data with dialog in a different language.
- Sound alignment techniques that employ timing information are described.
- features and timing information of sound data generated from a first sound signal are identified and used to identify features of sound data generated from a second sound signal.
- the identified features may then be utilized to align portions of the sound data from the first and second sound signals to each other.
- FIG. 1 is an illustration of an environment in an example implementation that is operable to employ identification and alignment techniques as described herein.
- FIG. 2 depicts a system in an example implementation in which aligned sound data is generated from overdub sound data and reference sound data of FIG. 1 .
- FIG. 3 depicts a system in an example implementation in which features and timing information are utilized to generate aligned sound data.
- FIG. 4 is a flow diagram depicting a procedure in an example implementation in which features and timing information identified from sound data of a first sound signal are used to identify features from sound data of a second sound signal.
- FIG. 5 is a flow diagram depicting a procedure in an example implementation in which features are identified and used to align sound data.
- FIG. 6 illustrates an example system including various components of an example device that can be implemented as any type of computing device as described and/or utilize with reference to FIGS. 1-5 to implement embodiments of the techniques described herein.
- Sound alignment techniques may be employed to support a variety of different functionality. For example, sound data having a higher quality may be synchronized with sound data having a lower quality to replace the lower quality sound data, such as to remove noise from a video shoot, music recording, and so on. In another example, a foreign overdub may be used to replace original sound data for a movie with dialog in a different language.
- conventional auto-alignment systems may not be robust to noise, examples of which include use of dynamic time warping and hidden Markov models. This may be due to a variety of different complications, such as distortion of Mel-frequency cepstral coefficient (MFCC) values by the noise such that the values become indistinguishable from each other. Accordingly, conventional sound alignment techniques were not utilized in such situations as previously described.
- MFCC Mel-frequency cepstral coefficient
- Timing information Sound alignment techniques that involve use of timing information are described herein.
- features and timing information are extracted from overdub sound data that is to be used to replace at least part of reference sound data.
- the reference sound data may have been recorded in a noisy environment. Accordingly, overdub sound data may be captured to replace at least parts of the reference sound data, such as to have an actor repeat portions of the dialog.
- Other examples are also contemplated, such as use of a foreign overdub.
- the identified features and timing information from the overdub sound data may then be used to process the reference sound data to identify similar features based on the timing information. In this way, this processing may be performed by having an idea of “where to look” for the features based on the timing information and thus may improve accuracy as well as efficiency in processing of the data. Additional discussion of these and other techniques may be found in relation to the following sections.
- Example procedures are then described which may be performed in the example environment as well as other environments. Consequently, performance of the example procedures is not limited to the example environment and the example environment is not limited to performance of the example procedures.
- FIG. 1 is an illustration of an environment 100 in an example implementation that is operable to employ techniques described herein.
- the illustrated environment 100 includes a computing device 102 and sound capture devices 104 , 106 , which may be configured in a variety of ways.
- the computing device 102 may be configured as a desktop computer, a laptop computer, a mobile device (e.g., assuming a handheld configuration such as a tablet or mobile phone), and so forth.
- the computing device 102 may range from full resource devices with substantial memory and processor resources (e.g., personal computers, game consoles) to a low-resource device with limited memory and/or processing resources (e.g., mobile devices).
- a single computing device 102 is shown, the computing device 102 may be representative of a plurality of different devices, such as multiple servers utilized by a business to perform operations “over the cloud” as further described in relation to FIG. 6 .
- the sound capture devices 104 , 106 may also be configured in a variety of ways. Illustrated examples of one such configuration involves a standalone device but other configurations are also contemplated, such as part of a mobile phone, video camera, tablet computer, part of a desktop microphone, array microphone, and so on. Additionally, although the sound capture devices 104 , 106 are illustrated separately from the computing device 102 , the sound capture devices 104 , 106 may be configured as part of the computing device 102 , a single sound capture device may be utilized in each instance, and so on.
- the sound capture devices 104 , 106 are each illustrated as including respective sound capture modules 108 , 110 that are representative of functionality to generate sound data, examples of which include reference sound data 112 and overdub sound data 114 .
- Reference sound data 112 is utilized to describe sound data for which at least a part is to be replaced by the overdub sound data 114 . This may include replacement of noisy portions (e.g., due to capture of the reference sound data 112 “outside”), use of a foreign overdub, and so on.
- the overdub sound data 114 may reference unaligned sound data that is to be processed for alignment with the reference sound data 112 . Accordingly, although illustrated separately for clarity in the discussion it should be apparent that these roles may be satisfied alternately by different collections of sound data (e.g., in which different parts are taken from two or more files), and so on.
- this data may then be obtained by the computing device 102 for processing by a sound processing module 116 .
- a sound processing module 116 may be further divided, such as to be performed “over the cloud” via a network 118 connection, further discussion of which may be found in relation to FIG. 6 .
- the alignment module 120 is representative of functionality to align the overdub sound data 114 to the reference sound data 112 to create aligned sound data 122 . As previously described, this may be used to replace noisy portion of sound data, replace dialog with other dialog (e.g., for different languages), and so forth. Further discussion of generation of the aligned sound data 122 may be found in the following discussion and associated figure.
- FIG. 2 depicts a system 200 in an example implementation in which aligned sound data 122 is generated from overdub sound data 114 and reference sound data 112 from FIG. 1 .
- Overdub sound data 114 and reference sound data 112 are illustrated as being received for processing by respective extraction modules 202 , 204 of the alignment module 120 .
- a single extraction module may also be utilized for processing both the overdub sound data 114 and the reference sound data 112 .
- the extraction modules 202 , 204 are each illustrated as including a respective feature module 206 , 208 .
- the feature modules 206 , 208 are representative of functionality to identify features in the sound data that are usable to uniquely identify particular portions of the sound data.
- An example of one such feature includes speech characteristics of utterances made by one or more users, although other examples are also contemplated as further described in relation to FIG. 3 .
- the extraction modules 202 , 204 are also illustrated as including timing modules 210 , 212 , respectively.
- the timing modules 210 , 212 are representative of functionality to identify timing information 214 for respective features 216 as well as to locate features 214 based at least in part on the timing information 216 .
- the overdub sound data 114 may be processed by the feature module 206 to identify features 214 and the timing module 210 to identify timing information 216 for those features.
- the identified features 214 and the timing information 216 may then be passed to the extraction module 204 to process the reference sound data 112 .
- the feature module 208 and the timing module 212 may leverage the prior knowledge provided by the identification of the features 214 and timing information 216 from the overdub sound data 114 to locate features 218 in the reference sound data 112 .
- the features identified in the overdub sound data 114 and the features 218 identified from the reference sound data 112 may then be used by a synthesis module 220 to generate aligned sound data 112 . This may include “speeding up” and “slowing down” portions of the overdub sound data 114 to match feature timing in the reference sound data 112 .
- Feature identification and timing information extraction may be performed in a variety of ways, an example of which is described as follows and shown in an associated figure.
- FIG. 3 depicts a system 300 in an example implementation in which features and timing information are utilized to generate aligned sound data.
- a reference sound signal 302 and an overdub sound signal 304 are processed by a time/frequency transform module 306 to create reference sound data 112 and overdub sound data 114 , which may be configured in a variety of ways.
- the sound data may form one or more spectrograms of a signal of a respective signal.
- a time-domain signal may be received and processed to produce a time-frequency representation, e.g., a spectrogram.
- the reference sound data 112 and overdub sound data 114 provide a time-frequency representation of the reference sound signal 302 and overdub sound signal 304 , respectively, in this example.
- Spectrograms may be generated as magnitudes of short time Fourier transforms (STFT) of the signals.
- STFT short time Fourier transforms
- the spectrograms may assume a variety of configurations, such as narrowband spectrograms (e.g., 32 ms windows) although other instances are also contemplated.
- the STFT subbands may be combined in a way so as to approximate logarithmically-spaced and other nonlinearly-spaced subbands. In doing so, potentially adverse effects (e.g., very dissimilar features) from differences in pitch between the two sound recordings may be mitigated and small differences in pitch may not result in significant differences in features, e.g., spectral basis vectors, weights.
- STFTs and subband representations may be calculated for each of the reference sound signal 302 and overdub sound signal 304 before computing respective features, although other implementations are also contemplated.
- the overdub sound data 114 is then received by a feature module 206 to identify features 214 that are usable to identify particular parts of the overdub sound data 114 for alignment purposes.
- This may include calculation of bases 308 (e.g., spectral characteristics) and weights 310 (e.g., temporal features) of the overdub sound data 114 .
- features 214 may include spectral features such as spectral basis vectors, which may be spectral building blocks of the sound data.
- features 214 may also include weights 310 involving temporal features, such as speech weights, noise weights, and so on. The weights may define a temporal evolution of a signal such that at each time instance of the signal, the signal may be defined by a linear combination of the blocks.
- the feature module 206 may employ a variety of different techniques to compute the features 214 .
- the features 214 may be computed with an algorithm, such as Probabilistic Latent Component Analysis (PLCA), nonnegative matrix factorization (NMF), nonnegative hidden Markov (N-HMM), nonnegative factorial hidden Markov (N-FHMM), and the like.
- PLCA Probabilistic Latent Component Analysis
- NMF nonnegative matrix factorization
- N-HMM nonnegative hidden Markov
- N-FHMM nonnegative factorial hidden Markov
- N speech ” speech basis vectors and weights may be computed.
- PLCA may be used to model data (e.g., a sound recording) as a multidimensional joint probability distribution.
- data e.g., a sound recording
- P r (f,t) e.g., non-stationary noise
- the PLCA model may operate on the spectrogram representation of the audio data and may learn an additive set of basis functions that represent each of the potential spectral profiles expected from a sound.
- the observed time-frequency magnitude distribution “P(f,t)” may be expressed as a normalized magnitude spectrogram of a signal as follows:
- X N ⁇ ( f , t ) ⁇ X ⁇ ( f , t ) ⁇ ⁇ f , t ⁇ ⁇ ⁇ X ⁇ ( f , t ) ⁇ with “X(f,t)” being a short-time Fourier transform of a signal and “X N (f,t)” being the normalized STFT.
- PLCA may then enable the hidden, or latent, components of the data to be modeled as the three distributions as follows:
- model parameters may be estimated using an expectation-maximization (EM) algorithm.
- EM expectation-maximization
- each of the components is implicitly nonnegative through modeling as distributions. Accordingly, by using nonnegative components, the components may all be additive, which can result in more intuitive models.
- Prior knowledge of the signal may be used, such as incorporating entropic priors for sparsity, and adding temporal coherence through hidden Markov models.
- other models may also be used.
- non-probabilistic models such as non-negative matrix factorization (NMF), the nonnegative hidden Markov model (N-HMM), and the nonnegative factorial hidden Markov model (N-FHMM) may also be used.
- NMF non-negative matrix factorization
- N-HMM nonnegative hidden Markov model
- N-FHMM nonnegative factorial hidden Markov model
- other techniques may also be employed by the system 300 , such as to employ an NMF, N-HMM, or N-FHMM framework.
- overdub sound data 114 may be represented using a spectrogram (e.g., magnitude subband representation), which may be calculated from the overdub sound signal 304 .
- PLCA may then be performed on the spectrogram of the overdub sound data 114 .
- the speech basis vectors learned from overdub sound data 114 may be reused as the speech basis vectors for processing the reference sound data 1122 by the feature module 208 to arrive at features 218 as further described below.
- the timing module 210 may also be used to compute timing information 216 as previously described.
- the timing information 216 is configured as a transition matrix 312 of the weights 310 . This is performed by computing a cross-correlation of the weights 310 , such as a correlation of the “n-th” frame's weights with the weights in the “n+1-th” frame for each of the frames in the overdub sound data 114 .
- Outputs of the feature module 206 and timing module 210 may then be provided to the feature module 208 for processing of the reference sound data 112 .
- the reference sound data 112 may be a recording of the same speaker from the overdub sound data 114 (e.g., a same actor/actress), the same musical instrument, a different speaker (e.g., foreign language recording, two different singers each singing the same song), a different musical instrument (e.g., playing the same song as the musical instrument from the overdub sound signal 304 ), or a same or different musical performer, and so on.
- the reference sound data 112 may also be configured as a time-frequency representation, such as a spectrogram.
- the reference sound data 112 may then be processed by the feature module 208 to arrive at a collection of features 218 .
- the feature module 208 may also leverage the features 214 and timing information 216 generated by the feature module 206 and timing module 210 from the overdub sound data 114 .
- the feature module 208 may employ PLCA or another technique to compute weights using the bases 208 of the overdub sound data 114 . Additional bases may be added in order to account for and estimate noise. In this case, the bases for the noise and the weights for both speech and noise are estimated, with the bases for the speech fixed. The weights corresponding to the speech are used as the features 218 for the reference sound data 112 .
- the feature module 208 may also employ an output of the timing module 210 in the identification of the features 218 by using timing module 212 . In each iteration, after each initial guess of the weights is performed by the feature module 208 , that guess and the transition matrix are used to estimate a new set of weights.
- the feature module 208 may employ the PLCA algorithm such that an update of the noise basis vectors is allowed to adapt to the noise but the speech basis vectors are kept constant.
- this technique may be employed to address a “noisy” signal.
- these techniques may be adjusted when the reference sound data 112 has little to no noise. For instance, if it is known that the reference sound data 112 has little to no noise, PLCA may be performed to find a new “P r (t)” and “P r (z
- the reference features may then be computed similarly resulting in “P r (z,t).” Because the same basis set may be used for both the overdub sound data 114 and the reference sound data 112 , parts of audio similar in the second signal may have values of “P r (z
- enhanced reference sound data may be synthesized by performing semi-supervised source separation based on the speech basis vectors and weights.
- features for the enhanced reference sound data may be computed based on the computed features 214 from the overdub sound data 114 , or in other instances, independently without using the computed features 214 . Additionally, independent computation of features may also be performed using algorithms other than PLCA.
- Aligned sound data 122 may then be generated based on the features output for the overdub sound data 114 and the reference sound data 112 .
- An adjustment and synthesis module 220 may be used to time align a temporal portion of the features 214 of the overdub sound data 114 with a temporal portion of the features 218 of the reference sound data.
- the features 214 , 218 may each include matrices of speech weights for the overdub sound data 114 and the reference sound data 112 , respectively. Basis vectors and noise weights may be discarded.
- the features 214 , 218 may be used to analyze how the overdub sound signal 304 may be warped in time by the time warping module 314 to align the respective features, such as by a global offset or sampling factor, compressing, stretching, and so on.
- the time warping module 314 may employ dynamic time warping that leverages a similarity matrix of the reference and overdub features, respectively.
- the similarity matrix may be configured in a variety of ways, such as a two-dimensional rectangular matrix. One dimension may express length, in number of windows, for the reference sound data 112 and the other dimension may be the length for the overdub sound data 114 . Each element of the matrix may give a distance between features, such as the cosine distance.
- An optimal path may then be determined to minimize the error between the features of the reference sound data 112 and overdub sound data 114 , respectively, such that the path is most similar in the most number of planes.
- a path may indicate that to align a given frame of the reference sound data 112 and overdub sound data 114 , the reference sound data 112 and the overdub sound data 114 are each to be advanced by a single frame.
- a path may indicate that the reference sound data 112 is to be advanced two frames and the overdub sound signal 304 is to remain on a current frame, i.e., is not to be advanced.
- the paths may indicate whether to stretch, compress, time-shift, or otherwise warp one of the signals to better match the other signal.
- the similarity matrix may calculate the cosine distance of the reference and unaligned feature vectors (e.g., temporal speech weights) at each time window as follows:
- the two signals may match well even if the two signals have different amplitude but similar spectral characteristics.
- the time warping module 314 may use the similarity matrix to calculate the path through the matrix that results in the highest similarity score, and thus the similarity matrix may exhibit a proper path for alignment.
- a synthesis module 316 may then leverage an output of the time warping module 314 to generate aligned sound data 112 using the overdub sound data 114 and the reference sound data 112 .
- the overdub sound data 114 may be configured in a variety of ways.
- the system 300 may allow for the audio in one signal to more closely follow the other signal (e.g., second signal, reference signal) such that utterances or other audio overlap more closely.
- certain audio features from the two signals may be stretched, compressed, or shifted such that the lengths of those features are same and overlap in time.
- the system 300 may be used to automatically align the signals from the two saxophones to be more closely synchronized.
- frequency shift-invariant basis vectors may be utilized by incorporating shift-invariant PLCA.
- accuracy in the analysis of noisy reference sound data 112 may be increased by using knowledge of similarities with another signal through machine learning. Further, by exploiting knowledge of the other signal in analyzing the noise, introduction of artifacts at the feature computation level may be minimized. Moreover, by modeling the noise of the noisy reference signal separately, alignment to a high fidelity unaligned signal may be performed with increased accuracy.
- FIG. 4 depicts a procedure 400 in an example implementation in which features and timing information identified from sound data of a first sound signal are used to identify features from sound data of a second sound signal.
- Features and timing information are identified of sound data generated from a first sound signal (block 402 ).
- the features for instance, may be utilized to uniquely identify particular portions of the sound data and the timing information may help define where those features were found, temporally.
- features of the sound data generation from the first sound signal may include bases that describe spectral characteristics of the sound data and weights that describe temporal features of the sound data (block 404 ). Additionally, timing information may be computed as a cross-correlation of the weights for different frames in the sound data generated from the first sound signal (block 406 ).
- Features of sound data generated from a second sound signal are identified using the identified features and timing information of the sound data generated from the first sound signal (block 408 ). For example, a new set of weights may be estimated for the features of the sound data generated from the second sound signal using an estimate of weights along with the timing information (block 410 ). In this way, the timing information may aid in locating the features by knowing “where to look” for the features as further described above.
- FIG. 5 depicts a procedure 500 in an example implementation in which features are identified and used to align sound data.
- Features of sound data are identified that was generated from a second sound signal using features and timing information identified from sound data generated from a first sound signal (block 502 ).
- the first sound signal may be configured as an overdub sound signal 304 that is to be used to replace at least a portion of a reference sound signal 302 .
- features and timing information located for the overdub sound data 114 may be utilized to locate features in the reference sound data 112 .
- the overdub sound data 114 may be configured in a variety of different ways, such as a foreign overdub, different instrument, or originate from any other sound signal.
- Aligned sound data is generated using the identified features of the sound data from the first sound signal and the identified features of the sound data from the second sound signal (block 508 ).
- the alignment may involve stretching and/or compressing portions of the sound data for the first or second sound signals to align the features, an example of which is dynamic time warping. Other examples are also contemplated without departing from the spirit and scope thereof.
- FIG. 6 illustrates an example system generally at 600 that includes an example computing device 602 that is representative of one or more computing systems and/or devices that may implement the various techniques described herein. This is illustrated through inclusion of the sound processing module 116 , which may be configured to process sound data, such as sound data captured by an sound capture device 104 .
- the computing device 602 may be, for example, a server of a service provider, a device associated with a client (e.g., a client device), an on-chip system, and/or any other suitable computing device or computing system.
- the example computing device 602 as illustrated includes a processing system 604 , one or more computer-readable media 606 , and one or more I/O interface 608 that are communicatively coupled, one to another.
- the computing device 602 may further include a system bus or other data and command transfer system that couples the various components, one to another.
- a system bus can include any one or combination of different bus structures, such as a memory bus or memory controller, a peripheral bus, a universal serial bus, and/or a processor or local bus that utilizes any of a variety of bus architectures.
- a variety of other examples are also contemplated, such as control and data lines.
- the processing system 604 is representative of functionality to perform one or more operations using hardware. Accordingly, the processing system 604 is illustrated as including hardware element 610 that may be configured as processors, functional blocks, and so forth. This may include implementation in hardware as an application specific integrated circuit or other logic device formed using one or more semiconductors.
- the hardware elements 610 are not limited by the materials from which they are formed or the processing mechanisms employed therein.
- processors may be comprised of semiconductor(s) and/or transistors (e.g., electronic integrated circuits (ICs)).
- processor-executable instructions may be electronically-executable instructions.
- the computer-readable storage media 606 is illustrated as including memory/storage 612 .
- the memory/storage 612 represents memory/storage capacity associated with one or more computer-readable media.
- the memory/storage component 612 may include volatile media (such as random access memory (RAM)) and/or nonvolatile media (such as read only memory (ROM), Flash memory, optical disks, magnetic disks, and so forth).
- the memory/storage component 612 may include fixed media (e.g., RAM, ROM, a fixed hard drive, and so on) as well as removable media (e.g., Flash memory, a removable hard drive, an optical disc, and so forth).
- the computer-readable media 606 may be configured in a variety of other ways as further described below.
- Input/output interface(s) 608 are representative of functionality to allow a user to enter commands and information to computing device 602 , and also allow information to be presented to the user and/or other components or devices using various input/output devices.
- input devices include a keyboard, a cursor control device (e.g., a mouse), a microphone, a scanner, touch functionality (e.g., capacitive or other sensors that are configured to detect physical touch), a camera (e.g., which may employ visible or non-visible wavelengths such as infrared frequencies to recognize movement as gestures that do not involve touch), and so forth.
- Examples of output devices include a display device (e.g., a monitor or projector), speakers, a printer, a network card, tactile-response device, and so forth.
- the computing device 602 may be configured in a variety of ways as further described below to support user interaction.
- modules include routines, programs, objects, elements, components, data structures, and so forth that perform particular tasks or implement particular abstract data types.
- module generally represent software, firmware, hardware, or a combination thereof.
- the features of the techniques described herein are platform-independent, meaning that the techniques may be implemented on a variety of commercial computing platforms having a variety of processors.
- Computer-readable media may include a variety of media that may be accessed by the computing device 602 .
- computer-readable media may include “computer-readable storage media” and “computer-readable signal media.”
- Computer-readable storage media may refer to media and/or devices that enable persistent and/or non-transitory storage of information in contrast to mere signal transmission, carrier waves, or signals per se. Thus, computer-readable storage media refers to non-signal bearing media.
- the computer-readable storage media includes hardware such as volatile and non-volatile, removable and non-removable media and/or storage devices implemented in a method or technology suitable for storage of information such as computer readable instructions, data structures, program modules, logic elements/circuits, or other data.
- Examples of computer-readable storage media may include, but are not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical storage, hard disks, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or other storage device, tangible media, or article of manufacture suitable to store the desired information and which may be accessed by a computer.
- Computer-readable signal media may refer to a signal-bearing medium that is configured to transmit instructions to the hardware of the computing device 602 , such as via a network.
- Signal media typically may embody computer readable instructions, data structures, program modules, or other data in a modulated data signal, such as carrier waves, data signals, or other transport mechanism.
- Signal media also include any information delivery media.
- modulated data signal means a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal.
- communication media include wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, RF, infrared, and other wireless media.
- hardware elements 610 and computer-readable media 606 are representative of modules, programmable device logic and/or fixed device logic implemented in a hardware form that may be employed in some embodiments to implement at least some aspects of the techniques described herein, such as to perform one or more instructions.
- Hardware may include components of an integrated circuit or on-chip system, an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), a complex programmable logic device (CPLD), and other implementations in silicon or other hardware.
- ASIC application-specific integrated circuit
- FPGA field-programmable gate array
- CPLD complex programmable logic device
- hardware may operate as a processing device that performs program tasks defined by instructions and/or logic embodied by the hardware as well as a hardware utilized to store instructions for execution, e.g., the computer-readable storage media described previously.
- software, hardware, or executable modules may be implemented as one or more instructions and/or logic embodied on some form of computer-readable storage media and/or by one or more hardware elements 610 .
- the computing device 602 may be configured to implement particular instructions and/or functions corresponding to the software and/or hardware modules. Accordingly, implementation of a module that is executable by the computing device 602 as software may be achieved at least partially in hardware, e.g., through use of computer-readable storage media and/or hardware elements 610 of the processing system 604 .
- the instructions and/or functions may be executable/operable by one or more articles of manufacture (for example, one or more computing devices 602 and/or processing systems 604 ) to implement techniques, modules, and examples described herein.
- the techniques described herein may be supported by various configurations of the computing device 602 and are not limited to the specific examples of the techniques described herein. This functionality may also be implemented all or in part through use of a distributed system, such as over a “cloud” 614 via a platform 616 as described below.
- the cloud 614 includes and/or is representative of a platform 616 for resources 618 .
- the platform 616 abstracts underlying functionality of hardware (e.g., servers) and software resources of the cloud 614 .
- the resources 618 may include applications and/or data that can be utilized while computer processing is executed on servers that are remote from the computing device 602 .
- Resources 618 can also include services provided over the Internet and/or through a subscriber network, such as a cellular or Wi-Fi network.
- the platform 616 may abstract resources and functions to connect the computing device 602 with other computing devices.
- the platform 616 may also serve to abstract scaling of resources to provide a corresponding level of scale to encountered demand for the resources 618 that are implemented via the platform 616 .
- implementation of functionality described herein may be distributed throughout the system 600 .
- the functionality may be implemented in part on the computing device 602 as well as via the platform 616 that abstracts the functionality of the cloud 614 .
Abstract
Description
with “X(f,t)” being a short-time Fourier transform of a signal and “XN(f,t)” being the normalized STFT. PLCA may then enable the hidden, or latent, components of the data to be modeled as the three distributions as follows:
-
- “P(fÅz)” corresponds to the spectral building blocks, or basis vectors, of a signal;
- “P(z|t)” corresponds to how a weighted combination of these basis vectors may be combined at each time “t” to approximate an observed signal;
- P(z) corresponds to the relative contribution of each base to the entire observed signal.
Each distribution may be discrete.
F u(z,t)=P u(z,t)=P u(z|t)P u(t), for zεZ u
where “Zu” is a set of bases 308 (e.g., speech basis vectors) learned in the
F u(z,t)=P u(z,t)=P u(z|t)P u(t), for zεZ u
Thus, as before this technique may be employed to address a “noisy” signal.
“Tr” and “Tu” may be the number of windows in time of the reference and overdub
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